Coulomb's law

Coulomb's law describes the electric force between two point charges with the same mathematical shape as Newton's law of gravitation: proportional to the product of the two sources, inversely proportional to the square of the distance between them. F = kq₁q₂/r², with k the Coulomb constant. The resemblance is not superficial — both are inverse-square laws because both describe an influence spreading out from a point through three-dimensional space, so intensity dilutes as the surface area of an expanding sphere, which grows as r².

The inverse-square part is where intuition needs correcting. Tripling the distance does not divide the force by three; it divides it by nine, because the force depends on 1/r², not 1/r. Small changes in separation therefore produce large changes in force, which is why charged particles feel almost nothing at a distance and violently strong forces up close.

Unlike gravity, which only attracts, the Coulomb force can attract or repel, and the rule is simple: like charges repel, opposite charges attract. It is worth resisting the instinct to read "like" as "belongs together" — two positive charges are alike in sign and push each other away precisely because they are alike. And exactly as with gravity, the force is mutual: whatever force charge A exerts on charge B, charge B exerts back on A with equal magnitude and opposite direction, Newton's third law applying here just as it does to any other force.